The reciprocal of a fraction less than 1 is always a fraction greater than 1. Why is this?

Answers

Answer 1

Answer: Let's see, an example of a reciprocal of a fraction less than 1 would be something like this: 1/8, after the reciprocal it will become 8/1.
8/1 equals 8 therefore is larger than 1.

This will always happen because as long as the denominator(the bottom) is larger than the numerator, the reciprocal(flipping the numbers) will make it larger than 1.
Here are some examples of reciprocals: 1/2 becomes 2/1. 1/3 becomes 3/1. 1/4 becomes 4/1. Just swap the two numbers and the number that it becomes will be automatically larger than 1.

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Which statements are true about the polynomial 4x3 – 6x2 + 8x – 12? Check all that apply.
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2.The terms 4x3 and – 6x2 have a common factor.
3.The polynomial is prime. The factored polynomial is (2x2 – 3)(2x + 4).
4. The polynomial can be grouped in different ways to factor by grouping.

Answers

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2. correct- factor: 4

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Answers

Answer:

The correct prove will be:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$ $= (1)/(8)$

Step-by-step explanation:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$

Multiply and Divide by $2cos((\pi )/(14))$

= $(2sin((\pi )/(14))cos((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14)))/(2cos((\pi )/(14)))$

⇒ Let $(\pi )/(14)$ = Ф and 7Ф = $(\pi )/(2)$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$ $= (1)/(8)$

Keywords: prove, sinФ, cosФ

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You buy a bicycle helmet for $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is the original price

Answers

If you paid $22.26 after the discount and tax then 30% is 0.30 and 30% OFF is 1-0.30=0.70
Tax is 6% or 0.06 and along with the initial is 1+0.06=1.06 so P is original price in P×0.70×1.06=22.26
P×0.742=22.26
P=$30 was the original price

Answer:

$30

Step-by-step explanation:

$30

If n = 8 and 16 · 2^m = 4^(n – 8), then m = ?F. –4
G. –2
H. 0
J. 1
K. 8

Answers

$n = 8 , \n \n 16 \cdot 2^m = 4 ^(n - 8) \n \n 16 \cdot 2^m = 4 ^(8-8)\n \n 2^4 \cdot 2^m =(2^2 )^(0) \n \n2^(4+m)=2^0\n \n4+m=0 \n \nm=-4 \n \nAnswer : \ F. \ \ - 4$

Frank's Football Gear is having a sale on helmets. The sales price, not including tax is $125.50. If the sale is 30% off all helmets, what is the regular price of the helmet to the nearest cent?

Answers

The regular price for the football helmet would be $179.29.

a frog made three jumps the first was 12 5/6 the second was 8 3/6 the third jump was 15 1/6 inches what was the total distance the frog jump

Answers

The answer is 36 and 1/2

Turn them all into improper fractions 77/6 + 51/6 + 91/6 = 219/6 = 73/2

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